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Theorem dfsn2 4042
Description: Alternate definition of singleton. Definition 5.1 of [TakeutiZaring] p. 15. (Contributed by NM, 24-Apr-1994.)
Assertion
Ref Expression
dfsn2

Proof of Theorem dfsn2
StepHypRef Expression
1 df-pr 4032 . 2
2 unidm 3646 . 2
31, 2eqtr2i 2487 1
Colors of variables: wff setvar class
Syntax hints:  =wceq 1395  u.cun 3473  {csn 4029  {cpr 4031
This theorem is referenced by:  nfsn  4087  tpidm12  4131  tpidm  4134  preqsn  4213  opid  4236  unisn  4264  intsng  4322  snex  4693  opeqsn  4748  relop  5158  funopg  5625  f1oprswap  5860  fnprb  6129  enpr1g  7601  supsn  7951  prdom2  8405  wuntp  9110  wunsn  9115  grusn  9203  prunioo  11678  hashprg  12460  hashfun  12495  lubsn  15724  indislem  19501  hmphindis  20298  wilthlem2  23343  umgraex  24323  usgranloop0  24380  wlkntrllem1  24561  eupath2lem3  24979  1to2vfriswmgra  25006  preqsnd  27418  esumpr2  28074  wopprc  30972  dvh2dim  37172
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-un 3480  df-pr 4032
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